deletions | additions       diff --git a/vec_v_t_Delta_t__.tex b/vec_v_t_Delta_t__.tex  index 3c2ef64..567a6b8 100644  --- a/vec_v_t_Delta_t__.tex  +++ b/vec_v_t_Delta_t__.tex 
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$$\vec{v}(t- \Delta t) \Delta t + \frac{1}{2} \vec{a}(t- \Delta t) \Delta t^2 = \vec{x}(t) - \vec{x}(t - \Delta t)$$  $$\vec{v}(t) \Delta t + \frac{1}{2} \vec{a}(t) \Delta t^2 = \vec{x}(t+ \Delta t) - \vec{x}(t)$$ $$(\vec{v}(t- \Delta t) + \vec{v}(t)) \Delta t + \frac{1}{2} (\vec{a}(t- \Delta t)+ \vec{a}(t)) \Delta t^2 = \vec{x}(t + \Delta t) - \vec{x}(t - \Delta t)$$